Image reading apparatus

ABSTRACT

A plurality of image-forming optical elements are disposed such that a part of a field-of-view region of one image-forming optical element overlaps a part of a field-of-view region of an image-forming optical element disposed adjacent to the one image-forming optical element, each of the image-forming optical elements includes: a lens for collecting light scattered by a reading object; an aperture stop for cutting off some of the light collected by the lens; a phase modulating element for modulating phase of light passing through the aperture stop; and a lens for allowing the light whose phase is modulated by the phase modulating element to form an image on an image-forming surface, and the phase modulating elements are loaded such that resolution characteristics of the phase modulating elements in an arrangement direction of the image-forming optical elements are the same among the image-forming optical elements.

TECHNICAL FIELD

This disclosure relates image reading apparatuses for reading one ormore images of a reading object.

BACKGROUND ART

In an image reading apparatus used in, for example, a copier, a billreader, a scanner, a facsimile, etc., plural pairs of an image-forminglens and a linear image sensor are arranged in a main scanningdirection.

Each image-forming lens of the image reading apparatus collects lightscattered by a reading object which is moved in a sub-scanningdirection, and captures the collected light on an image-forming surfaceof a corresponding linear image sensor, and thereby forms an image ofthe reading object on the image-forming surface.

The linear image sensor of the image reading apparatus reads the imageformed by the image-forming lens.

The image-forming lenses arranged in the main scanning direction aredisposed such that a part of a field-of-view region of one image-forminglens overlaps a part of a field-of-view region of an image-forming lensdisposed adjacent to the one image-forming lens, and an image combiningprocess for the images respectively read by the linear image sensors isperformed, by which the images are overlapped. The field-of-view regionis a region in which the light scattered by the reading object iscollected.

CITATION LIST Patent Literatures

Patent Literature 1: JP 11-122440 A

SUMMARY OF INVENTION Technical Problem

Since the conventional image reading apparatus is configured in theabove-described manner, miniaturization of optical systems can beachieved by disposing small image-forming lenses. However, whenimage-forming lenses made of an inexpensive plastic are used to reducethe cost of the image-forming lenses, there is a problem that chromaticaberration occurs, degrading an image to be obtained.

In general, to suppress chromatic aberration occurring in theimage-forming lenses, glass materials having different refractiveindices and different dispersions are combined, but with inexpensiveplastic, correction of chromatic aberration is difficult, and thus, itis difficult to suppress chromatic aberration.

One or more embodiments of the present disclosure are made to solve aproblem such as that described above, and an object of one or moreembodiments in the present disclosure is to obtain an image readingapparatus capable of suppressing image degradation by suppressingchromatic aberration.

Solution to Problem

An image reading apparatus according to this disclosure includes:image-forming optical elements arranged in a straight line, eachimage-forming optical element for collecting light scattered by areading object and capturing the collected light on an image-formingsurface, and thereby forming an image of the reading object on theimage-forming surface; and imaging elements, disposed on theimage-forming surface, for reading respective images formed by theimage-forming optical elements, wherein the image-forming opticalelements are disposed such that a part of a field-of-view region of oneimage-forming optical element overlaps a part of a field-of-view regionof an image-forming optical element disposed adjacent to the oneimage-forming optical element, the field-of-view region being a regionin which the light scattered by the reading object is collected, eachimage-forming optical element includes: a lens for capturing the lightscattered by the reading object on the image-forming surface; anaperture stop for cutting off part of light passing through the lens;and a phase modulating element for modulating phase of light passingthrough the aperture stop, the phase modulating element havingresolution characteristics that depend on an angle around an opticalaxis, and the phase modulating elements are loaded such that resolutioncharacteristics of the phase modulating elements in an arrangementdirection of the image-forming optical elements are same among theimage-forming optical elements.

Advantageous Effects of Invention

According to one or more embodiments in the present disclosure, since aconfiguration is such that the phase modulating elements are loaded suchthat the resolution characteristics of the phase modulating elements inan arrangement direction of the image-forming optical elements are thesame among the image-forming optical elements, there is an advantageouseffect that chromatic aberration is suppressed, enabling the suppressionof image degradation.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a cross-sectional view showing an image reading apparatus inaccordance with Embodiment 1 of this application.

FIG. 2 is a perspective view showing the image reading apparatus ofEmbodiment 1 of this application.

FIG. 3 is a schematic diagram showing field-of-view regions of aplurality of image-forming optical elements 15.

FIG. 4 is an illustrative diagram showing axial chromatic aberrationoccurring in a refractive lens system.

FIG. 5 is a graph showing MTFs with respect to the distance to documentfor a case in which a phase modulating element 20 c is not loaded.

FIG. 6 is an illustrative diagram showing a phase modulation function.

FIG. 7A is an illustrative diagram showing collected rays for the casein which the phase modulating element 20 c is not loaded, and spotdiagrams at and near a position where the rays are collected. FIG. 7B isan illustrative diagram showing collected rays for a case in which thephase modulating element 20 c is loaded, and spot diagrams at and near aposition where the rays are collected.

FIG. 8 is a graph showing MTFs with respect to the distance to documentfor when the phase modulating element 20 c is loaded.

FIG. 9A is an illustrative diagram showing an MTF in an X-direction fora spot A, FIG. 9B is an illustrative diagram showing an MTF in theX-direction for a spot B, FIG. 9C is an illustrative diagram showing anMTF in the X-direction for a spot C, and FIG. 9D is an illustrativediagram showing an MTF in the X-direction for a spot D.

FIG. 10 is an illustrative diagram that defines directions used incomputing the MTF.

FIG. 11 is illustrative diagrams showing the results of computation ofMTFs for the case in which the angle θ is 0°, 30°, 45°, 60°, 90°, 120°,135°, 150°, and 180°.

FIG. 12A is an illustrative diagram showing an example in which globalcoordinates 40 and local coordinates 41 a, 41 b, 41 c, 41 d, 41 e, and41 f of phase superposition planes of all lenses 20 have the sameorientation, FIG. 12B is an illustrative diagram showing an example inwhich the local coordinates 41 a, 41 b, 41 c, 41 d, 41 e, and 41 f ofthe phase superposition planes of all lenses 20 are rotated by 45°, andFIG. 12C is an illustrative diagram showing an example in which thelocal coordinates 41 a, 41 b, 41 c, 41 d, 41 e, and 41 f of the phasesuperposition planes of all lenses 20 are rotated by θ.

FIG. 13 is an illustrative diagram showing an example in which a part ofthe lens 20 is cut.

FIG. 14A is an illustrative diagram showing an example in which a lens20 with θ=0° and a lens 20 with θ=270° are alternately disposed, FIG.14B is an illustrative diagram showing an example in which a lens 20with θ=0°, a lens 20 with θ=90°, a lens 20 with θ=180°, and a lens 20with θ=270° are disposed in this order from the left in the drawing,FIG. 14C is an illustrative diagram showing an example in which a lens20 with θ=0°, a lens 20 with θ=90°, a lens 20 with θ=180°, and a lens 20with θ=270° are randomly disposed, and FIG. 14D is an illustrativediagram showing an example in which a lens 20 including a first phasemodulating element 20 c whose loading angle around an optical axis has afirst direction and a lens 20 including a second phase modulatingelement 20 c whose loading angle around an optical axis has a seconddirection are alternately disposed.

FIG. 15A is an illustrative diagram showing the positions of images withno distortion and image shifted positions due to the WFC, and FIG. 15Bis an illustrative diagram showing the amounts of distortion forrespective positions in a main scanning direction.

FIG. 16 is a schematic diagram showing how an image formed by an nthimage-forming optical element 15 overlaps with an image formed by an(n+1)th image-forming optical element 15.

FIG. 17 is a cross-sectional view describing the features of an imagereading apparatus in accordance with Embodiment 4 of this application.

FIG. 18 is a cross-sectional view showing an example which is designedso as not to cause vignetting, with the same field-of-view regions asthose of FIG. 17 secured, in a system in which the image-forming opticalelements 15 a to 15 d are arranged in a line in the X-direction.

FIG. 19 is an illustrative diagram showing a document image in whichstraight lines are arranged in pitches p in the main scanning direction.

FIG. 20 is a schematic diagram showing behavior of rays at or near anoverlapping region 32 a on the reading object 1 side.

FIG. 21A is a ray tracing diagram for a case in which there is novignetting and there is no phase modulating element 20 c for the WFC,FIG. 21B is an illustrative diagram showing spot diagrams at animage-forming surface for the case of FIG. 21A, FIG. 21C is a raytracing diagram for a case in which the aperture width in theX-direction of a lens 18 is reduced to H from H′ to cause vignetting,FIG. 21D is an illustrative diagram showing spot diagrams at theimage-forming surface for the case of FIG. 21C, FIG. 21E is a raytracing diagram for a case in which there is no vignetting and there isa phase modulating element 20 c for the WFC, FIG. 21F is an illustrativediagram showing spot diagrams at the image-forming surface for the caseof FIG. 21E, FIG. 21G is a ray tracing diagram for a case in which thereis vignetting and there is a phase modulating element 20 c for the WFC,and FIG. 21H is an illustrative diagram showing spot diagrams at theimage-forming surface for the case of FIG. 21G.

FIG. 22A is an illustrative diagram showing distortion for the amount ofdefocus Z′=−2Δ, and FIG. 22B is an illustrative diagram showingdistortion for the amount of defocus Z′=+2Δ.

FIG. 23A is an illustrative diagram showing distortion in afield-of-view region 31 b for a case in which defocus Z=−2ΔM² occurs onthe reading object 1 side, FIG. 23B is an illustrative diagram showingdistortion in a field-of-view region 31 a for the case in which defocusZ=−2ΔM² occurs on the reading object side, FIG. 23C is an illustrativediagram showing distortion in the field-of-view region 31 b for a casein which defocus Z=+2ΔM² occurs on the reading object 1 side, and FIG.23D is an illustrative diagram showing distortion in the field-of-viewregion 31 a for when defocus Z=+2ΔM² occurs on the reading object 1side.

DESCRIPTION OF EMBODIMENTS

To describe this application in more detail, embodiments according tothis disclosure will be described below with reference to theaccompanying drawings.

Embodiment 1

FIG. 1 is a cross-sectional view showing an image reading apparatus inaccordance with Embodiment 1 of this application, and FIG. 2 is aperspective view showing the image reading apparatus in accordance withEmbodiment 1 of this application.

Although FIG. 1 is a cross-sectional view, hatching is not used in thedrawing because use of hatching makes it difficult to see the details ofthe drawing.

In FIGS. 1 and 2, a reading object 1 is placed on a top glass 11 of theimage reading apparatus. For example, in a scanner apparatus that scansa paper document or the like, which is the reading object 1, the readingobject is moved over the top glass 11 in a sub-scanning direction whichis a Y-direction in the drawing. In addition, in a business copier, theentire structure other than the top glass 11 shown in FIG. 1 is movedrelative to the reading object 1 placed still on the top glass 11, inthe sub-scanning direction which is the Y-direction in the drawing.

A light emitting unit 12 is a light source that emits light 13 towardthe reading object 1.

An image-forming system array 14 includes image-forming optical elements15.

The image-forming optical elements 15 each are arranged in a straightline. Namely, the image-forming optical elements 15 each are arranged ina main scanning direction, which is an X-direction in the drawing.

Although in the example of FIGS. 1 and 2 four image-forming opticalelements 15 are arranged, this is merely an example, and two or threeimage-forming optical elements 15 or five or more image-forming opticalelements 15 may be arranged.

The image-forming optical elements 15 are unit image-forming systemsthat are disposed in a line in the main scanning direction, and form, onan image-forming surface 22, reduced, transferred images of images of asurface of the reading object 1 by collecting light 16 scattered by thereading object 1 and imaging the collected light 17 on the image-formingsurface 22.

In addition, though details will be described later, the image-formingoptical elements 15 are disposed such that a part of a field-of-viewregion of one image-forming optical element 15 overlaps a part of afield-of-view region of an image-forming optical element 15 disposedadjacent to the one image-forming optical element 15. The field-of-viewregion is a region in which light 16 is collected.

Lenses 18 are first lenses that collect the light 16 scattered by thereading object 1.

Aperture stops 19 are optical parts that cut off some of the light 17collected by the lenses 18.

Lenses 20 each have a first lens surface 20 a on the aperture stop 19side and a second lens surface 20 b on the image-forming surface 22side, and a phase modulating element 20 c that modulates the phase ofrays passing through the aperture stop 19 is placed on the first lenssurface 20 a. The phase modulating element 20 c has resolutioncharacteristics that depend on an angle around an optical axis.

The lenses 20 each are a second lens that images light 21 whose phase ismodulated by a phase modulating element 20 c on the image-formingsurface 22.

Though details will be described later, the phase modulating elements 20c are loaded such that the resolution characteristics of the phasemodulating elements 20 c in an arrangement direction of theimage-forming optical elements 15 are the same among the image-formingoptical elements 15. Namely, the loading angles around the optical axesof the plurality of phase modulating elements 20 c relative to the mainscanning direction which is the X-direction are the same in the sameplane.

In the example of FIG. 1 the image reading apparatus includes the lenses18 and the lenses 20. However, because it is only required that thelight 16 scattered by the reading object 1 is captured on theimage-forming surface 22, the lenses 18 may have the function of thelenses 20 or the lenses 20 may have the function of the lenses 18.

A holder 23 is a holding member that holds the lenses 18 in theimage-forming optical elements 15.

A holder 24 is a holding member that holds the lenses 20 in theimage-forming optical elements 15.

Imaging elements 25 are linear-shaped chips disposed on theimage-forming surface 22. Each of the imaging elements 25 reads areduced, transferred image formed by a corresponding image-formingoptical element 15, and outputs the read reduced, transferred image, asan image of the reading object 1, to an image processor 60.

The image processor 60 performs an image combining process for combiningthe reduced, transferred images that are respectively outputted from theimaging elements 25. By scanning the reading object 1 on the top glass11 in the sub-scanning direction, which is the Y-direction, atwo-dimensional image of the surface of the reading object 1 isobtained.

FIG. 3 is a schematic diagram showing the field-of-view regions of theimage-forming optical elements 15.

In FIGS. 3, 31 a, 31 b, 31 c, and 31 d are the field-of-view regions ofthe image-forming optical elements 15. Although, in FIG. 3, in orderthat overlapping of the field-of-view regions can be easily seen, two(top and bottom) alternate layers are depicted on the paper, thefield-of-view regions actually overlap each other in a straight line.

For example, taking a look at the field-of-view region 31 b of animage-forming optical element 15 which is the second from the left inthe drawing, a part 32 a of the field-of-view region 31 b overlaps apart of the field-of-view region 31 a of an image-forming opticalelement 15 which is the first from the left, and a part 32 b of thefield-of-view region 31 b of the image-forming optical element 15 whichis the second from the left overlaps a part of the field-of-view region31 c of an image-forming optical element 15 which is the third from theleft.

The part 32 a of the field-of-view region 31 b that overlaps thefield-of-view region 31 a, and the part 32 b of the field-of-view region31 b that overlaps the field-of-view region 31 c are hereinafterreferred to as overlapping regions.

For example, assuming that an image reading range by the image readingapparatus is 300 mm, that the image-forming optical elements 15 aredisposed in 10 mm pitches in the X-direction, and that the range of thefield-of-view regions 31 a, 31 b, 31 c, 31 d is . . . 11 mm, the rangeof the overlapping regions 32 a, 32 b is . . . 1 mm.

Next, operation will be described.

The light emitting unit 12 gives off light 13 toward the reading object1 placed on the top glass 11.

The light 13 emitted from the light emitting unit 12 is scattered by thereading object 1. The light 16 scattered by the reading object 1 entersthe image-forming optical elements 15.

The lenses 18 in the image-forming optical elements 15 collect the light16 scattered by the reading object 1, and the aperture stops 19 in theimage-forming optical elements 15 cut off some of the light 17 collectedby the lenses 18.

The lenses 20 in the image-forming optical elements 15 capture the rayspassing through the aperture stops 19 on the image-forming surface 22,and thereby form on the image-forming surface 22 the reduced,transferred images of images of the surface of the reading object 1.

Note, however, that since the phase modulating elements 20 c are placedon the first lens surfaces 20 a of the lenses 20, the phases of the rayspassing through the aperture stops 19 are modulated by the phasemodulating elements 20 c. The operation of the phase modulating elements20 c will be described later.

The imaging elements 25 read the reduced, transferred images formed bythe image-forming optical elements 15, and output the read reduced,transferred images to the image processor 60.

When the image processor 60 receives the reduced, transferred imagesfrom the imaging elements 25, the image processor 60 performs an imagecombining process on the reduced, transferred images, and therebyoverlaps the reduced, transferred images. By scanning the reading object1 on the top glass 11 in the sub-scanning direction, which is theY-direction, a two-dimensional image of the surface of the readingobject 1 is obtained.

In Embodiment 1, the phase modulating elements 20 c are placed on thefirst lens surfaces 20 a of the lenses 20. When the phase modulatingelements 20 c are not loaded, it is difficult to suppress chromaticaberration occurring in the image-forming optical elements 15, and thus,it is difficult to suppress image degradation.

Image degradation occurring when the phase modulating elements 20 c arenot loaded will be specifically described below.

Here, it is assumed that the lens 20 does not have the first lenssurface 20 a such that the phase modulating element 20 c is placedthereon, but has only the second lens surface 20 b.

As general means for correcting chromatic aberration occurring in arefractive lens system such as the lens 20, there is known means thatuses an achromatic lens.

The achromatic lens is a lens in which a convex lens made of a glassmaterial with low dispersion and a concave lens made of a glass materialwith high dispersion are bonded together. Note, however, thatmanufacturing costs for bonded lenses with different materials are high.

Although manufacturing a achromatic lens using plastic reducesmanufacturing costs, the use of plastic makes it difficult to suppresschromatic aberration because correction of chromatic aberration isdifficult.

FIG. 4 is an illustrative diagram showing axial chromatic aberrationoccurring in a refractive lens system. The axial chromatic aberration isaberration in which the focus position varies between differentwavelengths.

In FIG. 4, B indicates converging blue light rays in the light passingthrough the aperture stop 19 and the lens 20, and forms an image at aposition close to the lens 20.

G indicates converging green light rays, and forms an image at aposition farther from the lens 20 than the converging blue light rays B.

R indicates converging red light rays, and forms an image at a positionfarther from the lens 20 than the converging green light rays G.

FIG. 5 shows modulation transfer function (MTF) graphs with respect tothe distance to document in a case in which the phase modulating element20 c is not loaded.

Here, the MTF is a transfer function of an optical system.

The reading object 1 which is an object targeted by the optical systemvaries in pattern and size, but can be considered as a collection ofpatterns ranging from a rough bright and dark pattern to a detailedbright and dark pattern. The MTF is a parameter for describing howfaithfully contrast which is these bright and dark patterns can bereproduced in an image.

FIG. 5 shows MTFs for a spatial frequency equivalent to 380 dpi, and thedistance to document on a horizontal axis is the distance to the readingobject 1 with reference to a just focused position. The MTF on avertical axis is shown for each R, G, B color.

Note that measurement of the MTF generally uses a sine-wave chart inwhich the light transmittance changes from 100% to 0% in a sine curvemanner, and the number of peaks of the sine wave present in 1 mm calleda spatial frequency.

In FIG. 5, the color R with a long wavelength has its peak in a positionof +0.15 mm, whereas the color B with a short wavelength has its peak ina position of −0.45 mm.

Hence, when a black and white document with a high spatial frequency isplaced in a position of +0.15 mm, red components are formed into animage without any blur, but blue components are blurred, resulting in animage with reddish white lines.

In addition, when a black and white document with a high spatialfrequency is placed in a position of −0.45 mm, blue components areformed into an image without any blur, but red components are blurred,resulting in an image with bluish white lines.

Therefore, it can be seen that, when the phase modulating element 20 cis not loaded, image degradation occurs, e.g., due to the fineness ofpatterns of an object, color looks blurred.

There is known a technique called wavefront coding (hereinafter,referred to as “WFC”) for suppressing image degradation by mounting thephase modulating element 20 c, and this technique is disclosed in, forexample, the following Patent Literature 2:

[Patent Literature 2] JP 2011-135484 A

The WFC is a technique in which the phase modulating element 20 c thatmodulates the phase of transmitted light is placed at or near anaperture stop, and in which image processing is performed on an imageread by an imaging element to reconstruct an image.

For phase modulation provided by the phase modulating element 20 c, forexample, phase modulation provided by a cubic phase-modulation functionsuch as that shown in Equation (1) below is conceivable:ϕ(X,Y)=a(X ³ +Y ³)  (1)

In Eq. (1), a is a constant. X is the position in the main scanningdirection and Y is the position in the sub-scanning direction. Note,however, that this is an example and thus phase modulations inaccordance with other functional forms are also conceivable.

For the phase modulating element 20 c, a plate member made oftransparent material, such as glass or plastic, and the plate member isprocessed such that a thickness Z thereof changes in accordance with theposition (X, Y) in a plane, as shown in Equation (2) below:Z=ϕ(X,Y)  (2)

A result of three-dimensional plotting of the function shown in Eq. (2)is as shown in FIG. 6. FIG. 6 is an illustrative diagram showing a phasemodulation function which is the function shown in Eq. (2).

By mounting the phase modulating element 20 c, collected rays aredistorted as shown in FIG. 7.

FIG. 7A illustrates collected rays for the case in which the phasemodulating element 20 c is not loaded, and also spot diagrams at andnear a position where the rays are collected.

FIG. 7B illustrates collected rays for the case in which the phasemodulating element 20 c is loaded, and also spot diagrams at and near aposition where the rays are collected.

When the phase modulating element 20 c is not loaded, as shown in FIG.7A, the size of a collected light spot changes greatly according todefocus from the focal point, and at the light collection point a smallspot is obtained, but by defocusing a bit a large spot is obtained.

By contrast, when the phase modulating element 20 c is loaded, as shownin FIG. 7B, a spot at a light collection point is also large and has anasymmetrically distorted shape, but substantially identical spots can beobtained regardless of the position in a Z-direction.

FIG. 8 is a graph diagram showing MTFs with respect to the distance todocument for the case in which the phase modulating element 20 c isloaded.

As in FIG. 5, FIG. 8 also shows the MTFs for a spatial frequencyequivalent to 380 dpi.

Comparison of FIGS. 5 and 8 shows that, in the case where the phasemodulating element 20 c is loaded, although peak values are small, MTFvalues are substantially constant against the change in the distance todocument.

Therefore, an image obtained when the phase modulating element 20 c isloaded is blurred in the same manner regardless of the position in theZ-direction, and thus, even if the amount of shift in the Z-direction isnot known, an image reconstructing process can be performed using thesame deconvolution filter. The image reconstructing process is disclosedin, for example, Patent Literature 3 below:

[Patent Literature 3] JP 2014-75653 A

In addition, a point spread function (hereinafter, referred to as “PSF”)which is obtained using the function shown in Eq. (1) has variousspatial frequency components. The PSF is an abbreviation for “PointSpread Function”.

FIG. 9 depicts illustrative diagrams showing MTFs in the X-direction forspots A to D in FIG. 7.

FIG. 9A is an illustrative diagram showing an MTF in the X-direction forthe spot A. FIG. 9B is an illustrative diagram showing an MTF in theX-direction for the spot B.

In addition, FIG. 9C is an illustrative diagram showing an MTF in theX-direction for the spot C, and FIG. 9D is an illustrative diagramshowing an MTF in the X-direction for the spot D.

For the spot A obtained in the case where the phase modulating element20 c is not loaded, as shown in FIG. 9A, the MTF has a large value overa wide spatial frequency range, and at the spot A an image with no bluris obtained.

For the spot B obtained in the case where the phase modulating element20 c is not loaded, as shown in FIG. 9B, since the MTF has a zero valueat two spatial frequencies, at the spot B some pieces of imageinformation in spatial frequency are lost, and thus, an imagereconstructing process using a deconvolution filter cannot be performed.

For the spots C and D obtained in the case where the phase modulatingelement 20 c is loaded, since the MTF does not have a zero value over awide spatial frequency range, an image reconstructing process using adeconvolution filter can be performed.

FIG. 9C showing the MTF in the X-direction for the spot C and FIG. 9Dshowing the MTF in the X-direction for the spot D are almost the samegraph, and there is an advantage in that the same deconvolution filtercan be used regardless of the distance in the Z-direction.

Note that the phase modulating element 20 c needs to be loaded in theplane of aperture stop so as to add the same modulation to point imagesat all image heights, which are positions in the X-direction. Inaddition, when there is a lens surface near the aperture stop, addingthe thickness Z, which is an amount of sag represented by Eq. (2), tothe shape of the lens curved surface provides the same phase modulationeffect.

Appling the WFC technique in this manner extends the depth of field ofeach of R, G, and B for each image-forming optical element 15, which isa unit image-forming system, and therefore differences in resolution forR, G, and B can be ignored and axial chromatic aberration is eliminatedin practice. In addition, not only the elimination of axial chromaticaberration, but also a great advantageous effect that the depth of fieldcan be increased over the case of not applying the WFC technique can beobtained.

Next, a problem occurring when the WFC is applied to a compound-eyeoptical system will be described.

When the WFC is applied to a linear image sensor of a compound-eyeoptical system scheme, due to the PSF having an asymmetric shape, aproblem occurs when images formed by the image-forming optical elements15, unit image-forming systems, are joined together.

Since the PSF has an asymmetric shape, the resolution of an image formedby the image-forming optical element 15 having the phase modulatingelement 20 c loaded thereon varies greatly depending on the direction.

FIG. 10 is an illustrative diagram that defines directions used when theMTF is computed.

In FIG. 10, θ is an angle from the X-direction.

FIG. 11 is an illustrative diagram showing the results of computation ofMTFs for cases in which the angle θ is 0°, 30°, 45°, 60°, 90°, 120°,135°, 150°, and 180°.

As shown in FIG. 11, the waveform of the MTF varies depending on theangle θ. Namely, the waveform of the MTF in the X-direction obtainedwhen the phase modulating element 20 c is rotated by an angle ϕ=−θ in anXY-plane is the MTF in an angular θ direction in FIG. 11. Hence, unlessthe same loading angle is set between the image-forming optical elements15, images with different resolution directions are joined together. Asa result, at boundaries where the images are joined together,significant image degradation occurs, such as the occurrence ofdiscontinuous changes in resolution.

When discontinuous changes in resolution occur in images formed by theimage-forming optical elements 15, even if an image reconstructingprocess using a deconvolution filter is performed on the images, thedirectional dependence of resolution remains.

In addition, depending on the orientation of the phase modulatingelement 20 c, ringing that does not exist in an original image may occurby performing an image reconstructing process. Due to this, when thedegree of occurrence of ringing varies depending on the orientation ofthe phase modulating element 20 c, a degraded, joined image that is notsuitable for appreciation may be obtained.

Hence, in Embodiment 1, by setting the loading angles around the opticalaxes of the phase modulating elements 20 c included in all image-formingoptical elements 15 to be the same angle θ in the same plane,characteristics that depend on the loading angles around the opticalaxes of the phase modulating elements 20 c are made identical. In otherwords, the phase modulating elements 20 c are installed such that theresolution characteristics of the phase modulating elements 20 c, in anarrangement direction of the image-forming optical elements 15, are thesame among the image-forming optical elements 15.

Specifically, the orientations of the lenses 20, each having the phasemodulating element 20 c placed on the first lens surface 20 a, are allset to be in the same direction.

FIG. 12 is illustrative diagrams showing the lenses whose orientationsare all set to be in the same direction.

In FIG. 12, 40 indicates global coordinates, and 41 a, 41 b, 41 c, 41 d,41 e, and 41 f indicate local coordinates of phase superposition planesof the lenses 20 whose phase modulation is represented by Eq. (1). Thephase superposition planes refer to the first lens surfaces 20 a onwhich the phase modulating elements 20 c are placed.

FIG. 12A is an illustrative diagram showing an example in which theglobal coordinates 40 and the local coordinates 41 a, 41 b 41, c, 41 d,41 e, and 41 f of the phase superposition planes of all lenses 20 havethe same orientation.

In the example of FIG. 12A, because the image-forming optical elements15 all have the same directional dependence of resolution, the problemoccurring when images formed by the image-forming optical elements 15are joined together is resolved.

FIG. 12B is an illustrative diagram showing an example in which thelocal coordinates 41 a, 41 b, 41 c, 41 d, 41 e, and 41 f of the phasesuperposition planes of all lenses 20 are rotated by ϕ=45°, but thelocal coordinates 41 a, 41 b, 41 c, 41 d, 41 e, and 41 f of the phasesuperposition planes of all lenses 20 have the same orientation.

FIG. 12C is an illustrative diagram showing an example in which thelocal coordinates 41 a, 41 b, 41 c, 41 d, 41 e, and 4.1 f of the phasesuperposition planes of all lenses 20 are rotated by θ, but the localcoordinates 41 a, 41 b, 41 c, 41 d, 41 e, and 41 f of the phasesuperposition planes of all lenses 20 have the same orientation.

In the examples of FIGS. 12B and 12C, although the orientations of thelocal coordinates 41 a, 41 b, 41 c, 41 d, 41 e, and 41 f of the phasesuperposition planes of all lenses 20 differ from the orientation of theglobal coordinates 40, when the waveform of the MTF at the angle θ suchas that shown in FIG. 11 is defined by Equation (3) below, because theMTF is a value indicating how much each spatial frequency component iscontained at the angle θ, even if the angle θ is changed by 180°, theMTF has the same value. Namely, Equation (4) below holds true:MTF=f(θ)  (3)f(θ)=f(θ+180°)  (4)

Therefore, even if the local coordinates 41 a, 41 b, 41 c, 41 d, 41 e,and 41 f of the phase superposition planes of all lenses 20 are rotatedby ϕ, the MTF matches between the +X-direction and −X-direction of theglobal coordinates.

Hence, even if the local coordinates 41 a, 41 b, 41 c, 41 d, 41 e, and41 f of the phase superposition planes of all lenses 20 are rotated byϕ, the directivity of image resolution matches among all image-formingoptical elements 15. Needless to say, the rotation by ϕ also includes arotation by ϕ=45°.

Note that as means for setting the same orientation for the localcoordinates 41 a, 41 b, 41 c, 41 d, 41 e, and 41 f of the phasesuperposition planes of the lenses 20, means for making a cut in a partof each of the lenses 20 or in a part of each of the phase modulatingelements 20 c placed on the first lens surfaces 20 a of the lenses 20 isconceivable.

FIG. 13 is an illustrative diagram showing an example in which a cut ismade in a part of the lens 20.

In the example of FIG. 13, the lens 20 that is partially cut in D-shapeis shown, and fitting portions 50 of the holder 24 for the lenses 20have a D-shape. By changing the shape or size of the cut, the magnitudeof rotation can be changed.

When a part of each of the phase modulating elements 20 c placed on thefirst lens surfaces 20 a of the lenses 20 is cut, too, by changing theshape or size of the cut, the magnitude of rotation can be changed.

As is clear from the above, according to Embodiment 1, since aconfiguration is such that the phase modulating elements 20 c areinstalled so as to have identical characteristics that depend on theloading angles around the optical axes of the phase modulating elements20 c included in the image-forming optical elements 15, an advantageouseffect is provided that chromatic aberration is suppressed, enabling thesuppression of image degradation.

Namely, since a configuration is such that the phase modulationcharacteristics of all phase modulating elements 20 c are made identicalby setting the loading angles around the optical axes of the phasemodulating elements 20 c included in all image-forming optical elements15 to be the same angle θ in the same plane, the WFC can be applied tolinear image sensors of compound-eye optical system type. As a result,an excellent image whose axial chromatic aberration is corrected can beobtained, and the depth of field can greatly improve.

Embodiment 2

Although Embodiment 1 above shows that the loading angles around theoptical axes of the phase modulating elements 20 c included in allimage-forming optical elements 15 are set to be the same angle ϕ in thesame plane, Embodiment 2 describes that the difference between theloading angles around the optical axes in the same plane of the phasemodulating elements 20 c included in the image-forming optical elements15 is an integer multiple of 90 degrees.

FIG. 14 shows illustrative diagrams depicting examples in which theorientations of the lenses 20 having the phase modulating elements 20 cloaded thereon differ therebetween by an integer multiple of 90 degrees.

In FIG. 14, the lenses 20 in which the angle of rotation of the localcoordinates with respect to the global coordinates 40 is any of 0°, 90°,180°, and 270° are disposed.

Where the phase modulation function is represented as shown in Eq. (1)above, due to the fact that even if an X-coordinate and a Y-coordinateare switched, the function expression is the same and that, as shown inEq. (4), even if the angle θ is changed by 180°, the MTF has the samevalue, the waveform of the MTF in the angular θ direction is the samefor θ=0°, 90°, 180°, and 270°. Namely, Equation (5) below holds true:f(0°)=f(90°)=f(180°)=f(270°)   (5)

Thus, even if the lenses 20 are rotated by ϕ=0°, 90°, 180°, and 270°,because the directional dependence of the MTF does not change, excellentjoining of images is possible.

FIG. 14A is an illustrative diagram showing an example in which a lens20 with ϕ=0° and a lens 20 with ϕ=270° are alternately disposed.

In the disposition of FIG. 14A, the MTFs of all image-forming opticalelements 15 are exactly the same for the X-direction and Y-direction ofthe global coordinates 40. Thus, when the image processor 60 combinesimages formed by the image-forming optical elements 15, because theresolution directivities of all images match, excellent overlapping ofthe images can be performed.

FIG. 14B is an illustrative diagram showing an example in which a lens20 with ϕ=0°, a lens 20 with ϕ=90°, a lens 20 with ϕ=180°, and a lens 20with ϕ=270° are disposed in this order from the left in the drawing.

FIG. 14C is an illustrative diagram showing an example in which a lens20 with ϕ=0°, a lens 20 with ϕ=90°, a lens 20 with ϕ=180°, and a lens 20with ϕ=270° are randomly disposed.

As in the case of FIG. 14A, in the case of FIGS. 14B and 14C, too, theMTFs of all image-forming optical elements 15 are exactly the same forthe X-direction and Y-direction of the global coordinates 40. Thus, whenthe image processor 60 combines images formed by the image-formingoptical elements 15, because the resolution directivities of all imagesmatch, excellent overlapping of the images can be performed.

FIG. 14D is an illustrative diagram showing an example in which a lens20 including a first phase modulating element whose loading angle aroundan optical axis has a first direction and a lens 20 including a secondphase modulating element whose loading angle around an optical axis hasa second direction are alternately disposed.

The first direction is a direction defined by local coordinates 41 a, 41c, and 41 e, a first coordinate axis for the first direction is anX-direction of the local coordinates 41 a, 41 c, and 41 e, and a secondcoordinate axis for the first direction is a Y-direction of the localcoordinates 41 a, 41 c, and 41 e.

In addition, the second direction is a direction defined by localcoordinates 41 b, 41 d, and 41 f, a first coordinate axis for the seconddirection is an X-direction of the local coordinates 41 b, 41 d, and 41f, and a second coordinate axis for the second direction is aY-direction of the local coordinates 41 b, 41 d, and 41 f.

Therefore, the direction of the first coordinate axis for the seconddirection is a direction rotated by −90 degrees with respect to thefirst coordinate axis for the first direction, and the direction of thesecond coordinate axis for the second direction is a direction rotatedby +90 degrees with respect to the second coordinate axis for the firstdirection.

As in the case of FIG. 14A, in the case of FIG. 14D, too, thedirectional dependences of MTFs match, and in addition, an advantageouseffect such as that shown below can be obtained.

When the PSF is distorted by the phase modulating element 20 c byapplying the WFC, not only spot distortion, but also asymmetricdistortion of the entire image occurs.

FIG. 15 is illustrative diagrams showing asymmetric distortion caused bythe WFC.

FIG. 15A shows the positions of images with no distortion and positionsin which images are shifted due to the WFC.

In FIG. 15A, the symbol “∘” indicates the position of an image with nodistortion, and the symbol “▪” indicates a position in which an image isshifted due to the WFC.

Images in +X positions are shifted in a more positive direction, andimages in −X positions are also shifted in the positive direction.

When the amounts of shift in FIG. 15A are represented as the amounts ofdistortion in a graph with the amount of distortion obtained when animage is shifted in a direction away from a central position X=0 beinga + direction, FIG. 15B is obtained. FIG. 15B is an illustrative diagramshowing the amounts of distortion for respective positions in the mainscanning direction.

As shown in FIG. 15B, left-right asymmetric image distortion occurs.Namely, in an image formed by a single image-forming optical element 15,the transfer magnification differs between the positive and negativedirections of the main scanning direction.

When, with such distortion present, a given image-forming opticalelement 15 and its adjacent image-forming optical element 15 areoriented in the same direction as in Embodiment 1 above, even if animage in an overlapping region of the adjacent image-forming opticalelement 15 is attempted to be superimposed, since the transfermagnification is different, it is difficult to perform superimposition.

FIG. 16 is a schematic diagram showing how an image formed by an nthimage-forming optical element 15 overlaps an image formed by an (n+1)thimage-forming optical element 15.

In an example of FIG. 16, overlapping is performed by correlating imagesbetween an overlapping region B_(n), located at the right edge of an nthimage and an overlapping region A_(n+1) located at the left edge of an(n+1)th image, but since the two images have different transfermagnifications, it is difficult to perform overlapping.

However, when the lenses 20 are arranged as shown in FIG. 14D, in alloverlapping regions, the transfer magnification matches between adjacentimages.

Hence, when the lenses 20 are arranged as shown in FIG. 14D, byperforming the same overlapping processing as that of the Embodiment 1above, an excellent image whose axial chromatic aberration is correctedcan be obtained.

Embodiment 3

Embodiment 2 above shows an example in which an excellent image whoseaxial chromatic aberration is corrected is obtained by arranging thelenses 20 as shown in FIG. 14D.

This Embodiment 3 describes an example in which an excellent image whoseaxial chromatic aberration is corrected is obtained by eliminatingasymmetric distortion in the overlapping regions 32 a, 32 b . . . whichare both edge portions of the field-of-view regions 31 a, 31 b, 31 c, 31d i.e., left-right asymmetric distortion such as that shown in FIG. 15.

The image processor 60 performs distortion correction (hereinafter,referred to as “distortion correction”) on a plurality of images havingleft-right asymmetric distortion as shown in FIG. 15, i.e., a pluralityof reduced, transferred images outputted from the imaging elements 25,respectively, before performing an image combining process foroverlapping a plurality of images. The distortion correction itself is apublicly known technique and thus a detailed description thereof isomitted.

By the image processor 60 performing distortion correction, distortionin the overlapping regions 32 a, 32 b . . . which is included inreduced, transferred images outputted from the imaging elements 25 iscompensated for.

By this, there is no more difference in transfer magnification between,for example, the overlapping region B_(n) located at the right edge ofthe nth reduced, transferred image (image) and the overlapping regionA_(n+1) located at the left edge of the (n+1)th reduced, transferredimage (image) shown in FIG. 16.

The image processor 60 performs distortion correction on a plurality ofreduced, transferred images outputted from the imaging elements 25,respectively, and then performs an image combining process foroverlapping the reduced, transferred images having been subjected to thedistortion correction.

Since there is no more difference in transfer magnification between, forexample, the overlapping region B_(n) and the overlapping regionA_(n+1), an excellent image whose axial chromatic aberration iscorrected can be obtained.

Embodiment 4

A plurality of reduced, transferred images (images) read by the imagingelements 25, respectively, include images in which vignetting hasoccurred by the lenses 18.

Embodiment 4 describes an example in which the image processor 60performs an image combining process using images in regions in whichvignetting has occurred.

FIG. 17 is a cross-sectional view describing the features of an imagereading apparatus in accordance with Embodiment 4 of this disclosure,and in FIG. 17 the same reference signs as those of FIG. 1 indicate thesame or corresponding portions.

An example is shown in which the number of image-forming opticalelements 15 of FIG. 17 is four as in FIG. 1. In FIG. 17, for convenienceof description, the four image-forming optical elements 15 aredistinguished as an image-forming optical element 15 a, an image-formingoptical element 15 b, an image-forming optical element 15 c, and animage-forming optical element 15 d.

In addition, in FIG. 17, for simplification of the drawing, the lenses18 and lenses 20 included in the image-forming optical elements 15 a to15 d are represented by line segments, as lenses with no thickness.

As in Embodiment 1 above, the phase modulating elements 20 c are placedon the first lens surfaces 20 a of the lenses 20.

Although in FIG. 17 the image-forming optical elements 15 a to 15 d arepurposely depicted such that they are shifted relative to each other inthe Z-direction so that overlapping between the field-of-view regions 31a, 31 b, 31 c, and 31 d of the respective image-forming optical elements15 a to 15 d can be seen, in practice, there is no shift in theZ-direction.

In FIG. 17, the arrangement pitches between the image-forming opticalelements 15 a to 15 d are Lp.

In Embodiment 4, when the image processor 60 performs an image combiningprocess for, for example, a reduced, transferred image outputted from animaging element 25 provided for the image-forming optical element 15 aand a reduced, transferred image outputted from an imaging element 25provided for the image-forming optical element 15 b, the image processor60 compares the degrees of matching between an image in an overlappingregion of the reduced, transferred image for the image-forming opticalelement 15 a and an image in an overlapping region of the reduced,transferred image for the image-forming optical element 15 b. Hence, theoverlapping regions require a range of a minimum number of pixels ormore, e.g., 10 pixels or more.

First, in Embodiment 4, the reason that the image processor 60 performsan image combining process using images in regions in which vignettinghas occurred will be described.

In an image reading apparatus in which the image-forming opticalelements 15 a to 15 d are arranged in a line in the X-direction and theentire image is reconstructed by performing an image combining processfor a plurality of reduced, transferred images which are read by theimaging elements 25 provided for the image-forming optical elements 15 ato 15 d, the image-forming optical elements 15 a to 15 d need to beoptical systems close to telecentric on the side of the reading object1.

Namely, an angle α shown in FIG. 17, i.e., α which is an angle formed bythe Z-direction which is an optical axis and an outermost ray, needs tobe small.

Note, however, that because the outermost ray is a bundle of rays,strictly speaking, an angle formed by an angle of a ray running at thecenter of an outermost bundle of rays (hereinafter, referred to as“outermost principal ray”) and the optical axis is defined as the angleα.

FIG. 18 is a cross-sectional view showing an example which is designedso as not to cause vignetting, with the same field-of-view regions asthose of FIG. 17 secured, in a system in which the image-forming opticalelements 15 a to 15 d are arranged in a line in the X-direction.

The arrangement pitches between the image-forming optical elements 15 ato 15 d of FIG. 18 are Lp which is the same as that of FIG. 17.

The lenses 18 included in the image-forming optical elements 15 a to 15d of FIG. 18 are arranged in a line in the X-direction, and thus, theaperture width H in the X-direction of the lenses 18 is less than orequal to Lp.

When, under these conditions, the lenses 18 are designed so as not tocause vignetting, as shown in FIG. 18, α which is the angle formed bythe optical axis and the outermost principal ray is larger than that ofthe image reading apparatus of FIG. 17 in which vignetting occurs.

Hence, the image-forming optical elements 15 a to 15 d of FIG. 18 arenot optical systems close to telecentric, compared to the image-formingoptical elements 15 a to 15 d of FIG. 17.

In the case of non-telecentric optical systems, the transfermagnification of an image greatly changes by a slight change in thedistance to document.

For example, it is assumed that, as shown in FIG. 19, a document imagein which straight lines extending in the Y-direction, which is thesub-scanning direction, are repeatedly arranged in pitches p in theX-direction, which is the main scanning direction, is present in anoverlapping region. In addition, it is also assumed that the imagereading apparatus has a resolution at a spatial frequency (1/p).

FIG. 19 is an illustrative diagram showing the document image in whichthe straight lines are arranged in the pitches p in the main scanningdirection.

FIG. 20 is a schematic diagram showing a state of rays at or near theoverlapping region 32 a on the side of the reading object 1.

In FIG. 20, an outermost principal ray on the −X side 51 a of theimage-forming optical element 15 a and an outermost principal ray on the+X side 51 b of the image-forming optical element 15 b are depicted suchthat they are extended in the +Z-direction.

In FIG. 20, for the position Z=Z₀ which is a focus position 52 on theside of the reading object 1, a desired depth of field is ΔZ, a farthestobject position 54 in the depth of field is Z=Z₊, and a nearest objectposition 53 in the depth of field is Z=Z⁻.

Since the image-forming optical elements 15 a to 15 d of FIG. 18 cannotbe called optical systems close to telecentric, a field-of-view regionchanges between the position Z₊ and the position Z⁻ depending on theangle α formed by the optical axis and the outermost principal ray.

The overlapping region 32 a in which the field-of-view region 31 a ofthe image-forming optical element 15 a overlaps the field-of-view region31 b of the image-forming optical element 15 b has a width of X₊ in theposition Z₊, and has a width of X⁻ in the position Z⁻.

Hence, the overlapping region 32 a changes by ΔX in the depth of field,as shown in Equation (6) below:ΔX=X ₊ −X ⁻  (6)

The amount of change ΔX of the overlapping region 32 a shown in Eq. (6)can also be represented as shown in Equation (7) below:ΔX=2·ΔZ·tan α  (7)ΔZ=Z ₊ −Z ⁻  (8)

If the amount of change ΔX of the overlapping region 32 a exceeds thepitch p shown in FIG. 19, then when the image processor 60 performs animage combining process, two reduced, transferred images may be combinedwith the images shifted by the pitch p.

When two reduced, transferred images are combined with the imagesshifted by the pitch p, the two reduced, transferred images arediscontinuous at a boundary region thereof, significantly degradingimage quality.

When, as shown in Inequality (9), the amount of change ΔX of theoverlapping region 32 a is smaller than the pitch p, Inequality (10)below holds true:ΔX<p  (9)tan α<p/(2·ΔZ)  (10)

To satisfy Ineq. (10), it is desirable that the angle α be a smallvalue.

Note, however, that in practice, even if Ineq. (10) is not satisfied, animage combining process can be performed by taking into account not onlyan image in the overlapping region 32 a of interest, but also an imagein a region around the overlapping region 32 a. Even in that case, it isdesirable that the angle α be as small as possible because the number ofcandidates for an image combining position can be reduced.

To reduce the angle α, in an area at or near the edge of a field-of-viewregion of an image-forming optical element 15, there is a need to obtainan image in a region in which vignetting has occurred and use the imagein the region in an image combining process.

Next, an image combining process using an image in a region in whichvignetting has occurred will be described.

FIG. 21 is illustrative diagrams showing changes in spot diagrams due tovignetting in the lens 18.

FIG. 21A is a ray tracing diagram for a case in which there is novignetting and there is no phase modulating element 20 c for the WFC,and FIG. 21B shows spot diagrams at the image-forming surface for thecase of FIG. 21A. The aperture width in the X-direction of the lens 18of FIG. 21A is H′.

FIG. 21B shows, as spot diagrams at the image-forming surface, spotdiagrams for a just focused position Z′=0, and also spot diagrams fordefocused positions shifted by ±Δ in a Z′ direction from the justfocused position, and spot diagrams for defocused positions shifted by±2Δ. On the image-forming surface side, a direction going away from thelens 18 is defined as +Z′.

FIG. 21C is a ray tracing diagram for a case in which the aperture widthin the X-direction of the lens 18 is reduced to H from H′ to causevignetting, and FIG. 21D shows spot diagrams at the image-formingsurface for the case of FIG. 21C.

In spot diagrams for x1′ and x5′ with vignetting, an inner region islost upon negative-side defocusing, and an outer region is lost uponpositive-side defocusing.

In addition, in the case of FIG. 21C, because there is no asymmetry inthe X-direction, the spot diagrams for x1′ and the spot diagrams for x5′have shapes that are just reversed from each other with respect to theX-direction.

FIG. 21E is a ray tracing diagram for a case in which there is novignetting and there is a phase modulating element 20 c for the WFC, andFIG. 21F shows spot diagrams at the image-forming surface for the caseof FIG. 21E.

In FIG. 21B, the spot diameter greatly changes for defocusing, whereasin FIG. 21F, the spot diameter does not change almost at all fordefocusing. This is the same advantageous effect as that described inFIG. 7. In addition, it can also be seen that since there is novignetting in the field-of-view region, the spot diameter is almost thesame regardless of x1′ to x5′.

FIG. 21G is a ray tracing diagram for a case in which there isvignetting and there is a phase modulating element 20 c for the WFC, andFIG. 21H shows spot diagrams at the image-forming surface for the caseof FIG. 21G.

In FIG. 21G, the width of a reading region is the same as that of FIG.21E, and the aperture width in the X-direction of the lens 18 is H andis smaller than the aperture width H′ in the X-direction of the lens 18of FIG. 21E.

In FIG. 21H, particular attention should be paid to spot diagrams withvignetting and for defocused positions, which are spot diagrams (1),(2), (5), and (6) in the drawing.

In FIG. 21G, as in FIG. 21C, vignetting occurs in bundles of rayslocated on the outer side of the lens 18 among the outermost bundles ofrays.

Then, at the defocused position Z′=−2Δ, as in FIG. 21D, an inner ray oflight is vignetted. However, since a spot diagram is greatly andasymmetrically distorted by the phase modulating element 20 c, the spotshape greatly differs between (1) and (2). In (1), as in FIG. 21D, theshape is such that the inside is greatly vignetted, but in (2) there isalmost no change in spot shape caused by vignetting.

In addition, in the defocused position Z′=2Δ, there is almost no changein spot shape of (5), and the spot shape of (6) is greatly lost outward.

FIG. 22 illustrates diagrams showing distortion which occurs as imagedistortion.

FIG. 22A shows distortion for the amount of defocus Z′=−2Δ.

A dashed line is distortion with no vignetting and corresponds to FIGS.21E and 21F.

A solid line is distortion with vignetting and corresponds to FIGS. 21Gand 21H.

In a spot of (1) of FIG. 21H, since the inside is vignetted, theluminance centroid position of the spot is shifted outward. Thus, in asolid-line graph of FIG. 22A, the value of distortion increases near the+X end in the image position.

FIG. 225 shows distortion for the amount of defocus Z′=+2Δ, and since,as shown in FIG. 21H, an outer spot is vignetted, the value ofdistortion increases in a positive direction at the −X end in the imageposition in a solid-line graph.

When irregular distortion occurs near an edge of a field-of-view region,a problem occurs in combining of a plurality of images.

For example, it is assumed that defocus Z=−2ΔM² has occurred in theoverlapping region 32 a which is present at a boundary portion betweenthe image-forming optical element 15 a and the image-forming opticalelement 15 b shown in FIG. 17.

M is the transfer magnification of images obtained by the image-formingoptical elements 15 a and 15 b, and the longitudinal magnification in afocus direction is M².

Spot diagrams on the image-forming surface side correspond to spotdiagrams for defocus Z′=−2Δ in FIG. 21H. Thus, when defocus Z=−2ΔM² hasoccurred on the side of the reading object 1, graphs of distortion withthe position of the side of the reading object 1 on the horizontal axisare as shown in FIGS. 23A and 23B.

The reason that FIGS. 23A and 23B are left-right reversed from FIG. 22Ais because the images obtained by the image-forming optical elements 15are reversed.

FIG. 23A shows distortion in the field-of-view region 31 b, and FIG. 23Bshows distortion in the field-of-view region 31 a. At this time, theoverlapping region 32 a is at the right end of the graph of FIG. 23A andis at the left end of the graph of FIG. 23B.

In addition, when defocus Z=+2ΔM² has occurred on the side of thereading object 1, graphs of distortion with the position of the side ofthe reading object 1 on the horizontal axis are as shown in FIGS. 23Cand 23D.

The reason that FIGS. 23C and 23D are left-right reversed from FIG. 22Bis because the images obtained by the image-forming optical elements 15are reversed.

FIG. 23C shows distortion in the field-of-view region 31 b, and FIG. 23Dshows distortion in the field-of-view region 31 a. At this time, theoverlapping region 32 a is at the right end of the graph of FIG. 23C andis at the left end of the graph of FIG. 23D.

When the amount of defocus on the side of the reading object 1 changesdue to the presence of vignetting, as shown in FIGS. 23A, 235, 23C, and23D, the distortion value in the overlapping region 32 a greatlychanges.

In two images that are more greatly distorted due to the occurrence ofvignetting, because their distortion values greatly differ from eachother, it is highly likely that the two images are combined at a wrongposition, and thus, it is difficult to properly perform an imagecombining process.

Hence, in Embodiment 4, the image processor 60 performs distortioncorrection on the respective reduced, transferred images outputted fromthe imaging elements 25 before performing an image combining process.

As can be seen from FIG. 22, the distortion changes by the amount ofdefocus. If the amount of defocus is known by some kind of means, thendistortion is uniquely determined from the amount of defocus, and thus,correction of the distortion is performed.

For example, the amount of defocus can be known from the results of animage combining process.

As can be understood from Eq. (7), the amount of change ΔX of anoverlapping region which is distortion changes in proportion to theamount of defocus ΔZ.

Hence, the image processor 60 first performs an image combining processwithout performing distortion correction, and thereby calculates theamount of defocus ΔZ. Here, since distortion correction is notperformed, an image combining process may not be able to be properlyperformed, but it is possible to calculate a rough amount of defocus ΔZ.

Then, the image processor 60 estimates, using, for example, Eq. (7), theamount of change ΔX of an overlapping region from the calculated amountof defocus ΔZ, and performs distortion correction based on the amount ofchange ΔX.

The distortion correction is image processing for locally stretching orshrinking an image in accordance with the position X, wherein a region(image) where ΔX is positive is corrected to be reduced in theX-direction, while a region (image) where ΔX is negative is corrected tobe enlarged in the X-direction.

Finally, the image processor 60 performs an image combining process fora plurality of reduced, transferred images having been subjected to thedistortion correction.

By this, an excellent image can be reconstructed.

Here, the image processor 60 performs an image combining process for aplurality of reduced, transferred images having been subjected todistortion correction, but the image processor 60 may further perform afiltering process for reconstructing an image whose resolution isdegraded due to modulation of the light by using the phase modulatingelements 20 c.

A specific description is as follows.

In a region in which vignetting has occurred, as shown in FIG. 21H, theshape of the PSF greatly differs from that in a region in whichvignetting has not occurred. Hence, a method is considered in which animage in a region in which vignetting has occurred is used only in aprocess of searching for a matching position in an image combiningprocess, and is not used in a final combining image process.

However, when a region in which vignetting has occurred occupies a largeportion of an overlapping region, unless an image in the region in whichvignetting has occurred is also used in a final combining image process,an excellent image may not be able to be reconstructed.

Note, however, that a reconstructing process in the WFC greatly dependson the shape of the PSF. Hence, different filters are used in afiltering process for regions at and near both edges of an image and ina filtering process for a region at and near the center of the image.

For example, a filter used in a filtering process for regions such as(1) and (6) of FIG. 21H is different from a filter used in a filteringprocess for regions such as (3) and (4) of FIG. 21H.

As described above, since the amount of defocus can be known from theresults of an image combining process, the shape of a spot resultingfrom vignetting can be calculated using the amount of defocus.

Hence, the image processor 60 selects a filter to be used in a filteringprocess, based on the shape of a spot.

A filtering process in a reconstructing process in the WFC here is toperform a process using a deconvolution filter, a filtering function ischanged in accordance with an image height position X′ and the amount ofdefocus Z of an object. As described in Section [0016] of PatentLiterature 3, when the function of an obtained image is g(x, y), the PSFfunction is h(x, y), and the function of an original image is f(x, y),the function of an obtained image can be represented as shown in thefollowing equation (11):g(x,y)=h(x,y)*f(x,y)  (11)

In Eq. (11), * is the symbol representing convolution.

When both sides of Eq. (11) are Fourier-transformed, Eq. (11) isrepresented by the product of Fourier transforms as shown in Equation(12) below:G(ξ,η)=H(ξ,η)·F(ξ,η)  (12)

In Eq. (12), G(ξ, η), H(ξ, η), and F(ξ, η) are the Fourier transformedfunctions of g(x, y), h(x, y), and f(x, y), respectively.

Thus, a reconstructing process in the WFC for reconstructing theoriginal image function f(x) is to find f(x, y) by computingF(ξ,η)=G(ξ,η)/H(ξ,η)and further performing an inverse Fourier transform.

In Embodiment 4, the PSF function h(x, y) is not always constant, anddifferent functions are used based on the image height position X′ andthe amount of defocus Z of an object. The function may be continuouslychanged based on the image height position X′ and the amount of defocusZ of an object, but for simplification of a process, it is practical todivide a region into several regions and change the function for eachregion. For example, in FIG. 21H, only for the regions of (1) and (6)which are regions in which there is large vignetting and spot diagramsare largely lost, h(x, y) based on their respective spot diagrams isused, and for other regions, because spot diagrams are substantiallycommon, common h(x, y) based on the spot diagrams can be used.

According to Embodiment 4, by performing left-right asymmetricdistortion correction on an image in a region in which vignetting hasoccurred, the image in the region in which vignetting has occurred canalso be used in an image combining process. Hence, an advantageouseffect can be obtained that even with the angle α formed by an opticalaxis and an outermost ray of light being small, the image-formingoptical elements 15 a, 15 b, 15 c, and 15 d are arranged in a line andsufficient overlapping regions for an image combining process can beobtained for the respective field-of-view regions.

In addition, since a filtering process that uses different filters inaccordance with a change in the shape of a spot caused by vignetting isperformed, a more excellent image can be reconstructed.

Note that a free combination of the embodiments, modifications to anycomponent in the embodiments, or omissions of any component in theembodiments are possible within the scope of the invention.

INDUSTRIAL APPLICABILITY

Disclosed embodiments are suitable for use as an image reading apparatusfor reading an image of a reading object.

REFERENCE SIGNS LIST

1: Reading object, 11: Top glass, 12: Light emitting unit, 13: Light,14: Image-forming system array, 15, 15 a, 15 b, 15 c, and 15 d:Image-forming optical element, 16 and 17: Light, 18: Lens, 19: Aperturestop, 20: Lens, 20 a: First lens surface, 20 b: Second lens surface, 20c: Phase modulating element, 21: Light, 22: Image-forming surface, 23and 24: Holder, 25: Imaging element, 31 a, 31 b, 31 c, and 31 d:Field-of-view region, 32 a and 32 b: Overlapping region, 40: Globalcoordinates, 41 a, 41 b, 41 c, 41 d, 41 e, and 41 f: Local coordinatesof phase superposition plane, 50: Fitting portion, 51 a: Outermostprincipal ray on the −X side, 15 b: Outermost principal ray on the +Xside, 52: Focus position on the reading object side, 53: Nearest objectposition in the depth of field, 54: Farthest object position in thedepth of field, and 60: Image processor.

The invention claimed is:
 1. An image reading apparatus comprising:image-forming optical elements arranged in a straight line, eachimage-forming optical element for collecting light scattered by areading object and capturing the collected light on an image-formingsurface, and thereby forming an image of the reading object on theimage-forming surface; and imaging elements, disposed on theimage-forming surface, for reading respective images formed by theimage-forming optical elements, wherein the image-forming opticalelements are disposed such that a part of a field-of-view region of oneimage-forming optical element overlaps a part of a field-of-view regionof an image-forming optical element disposed adjacent to the oneimage-forming optical element, the field-of-view region being a regionin which the light scattered by the reading object is collected, eachimage-forming optical element includes: a lens for capturing the lightscattered by the reading object on the image-forming surface; anaperture stop for cutting off part of light passing through the lens;and a phase modulating element for modulating phase of light passingthrough the aperture stop, the phase modulating element havingresolution characteristics that depend on an angle around an opticalaxis, and the phase modulating elements are loaded such that resolutioncharacteristics of the phase modulating elements in an arrangementdirection of the image-forming optical elements are same among theimage-forming optical elements.
 2. The image reading apparatus accordingto claim 1, wherein the lens includes a first lens for collecting thelight scattered by the reading object, and a second lens for capturingthe light whose phase is modulated by the phase modulating element onthe image-forming surface.
 3. The image reading apparatus according toclaim 2, wherein the second lens has a first lens surface provided so asto face the aperture stop, and a second lens surface provided so as toface the image-forming a surface, and the phase modulating element isplaced on the first lens surface.
 4. The image reading apparatusaccording to claim 3, wherein a cut is made in a part of each of thelenses having the phase modulating elements placed on the first lenssurfaces.
 5. The image reading apparatus according to claim 1, whereinloading angles around the optical axes of the phase modulating elementsare set to be a same angle in a same plane, the phase modulatingelements being included in the image-forming optical elements.
 6. Theimage reading apparatus according to claim 1, wherein a phase ϕ(X, Y)modulated by each of the phase modulating elements included in theimage-forming optical elements is represented by a function a(X³ +Y³)based on a constant a, a position X in a main scanning direction, and aposition Y in a sub-scanning direction.
 7. The image reading apparatusaccording to claim 1, wherein a difference between loading angles aroundthe optical axes in a same plane of the phase modulating elementsincluded in the image-forming optical elements is an integer multiple of90 degrees.
 8. The image reading apparatus according to claim 7, whereinas the phase modulating elements included in the image-forming opticalelements, a first phase modulating element whose loading angle around anoptical axis has a first direction and a second phase modulating elementwhose loading angle around an optical axis has a second direction arealternately disposed, and a direction of a first coordinate axis for thesecond direction is a direction rotated by -90 degrees with respect to afirst coordinate axis for the first direction, and a direction of asecond coordinate axis for the second direction is a direction rotatedby +90 degrees with respect to a second coordinate axis for the firstdirection.
 9. The image reading apparatus according to claim 1, whereina cut is made in a part of each of the phase modulating elementsincluded in the image-forming optical elements.
 10. The image readingapparatus according to claim 1, comprising an image processor forperforming an image combining process for overlapping the imagesrespectively read by the imaging elements.
 11. The image readingapparatus according to claim 10, wherein the images respectively read bythe imaging elements are images in which both edge portions of each ofthe field-of-view regions are asymmetrically distorted, and the imageprocessor performs a correction process for correcting the distortion ofthe images respectively read by the imaging elements, and then performsthe image combining process.
 12. The image reading apparatus accordingto claim 11, wherein the images respectively read by the imagingelements include an image with vignetting caused by a corresponding oneof the lenses, and the image processor performs the correction processby using the image in a region with vignetting.
 13. The image readingapparatus according to claim 10, wherein the images respectively read bythe imaging elements include an image with vignetting caused by acorresponding one of the lenses, the image processor performs afiltering process for reconstructing an image whose resolution isdegraded due to modulation of phase of light performed by acorresponding one of the phase modulating elements, and a filter used toperform the filtering process is different for different positions ofimages whose resolution is degraded.